Question

An arrow is shot vertically upward from a platform 8ft
high at a rate of 157ft/sec
. When will the arrow hit the ground? Use the formula: h=−16t2+v0t+h0
. (Round your answer to the nearest tenth.)

Answer 1

To find when the arrow will hit the ground, we need to find the time when the height is equal to 0.

Using the formula h = -16t^2 + v0t + h0, where h is the height, t is the time, v0 is the initial velocity, and h0 is the initial height, we can substitute the given values:

0 = -16t^2 + 157t + 8

Now, we can solve this quadratic equation to find the value of t. We can either factor it or use the quadratic formula. Let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac))/(2a)

In this equation, a is the coefficient of t^2 (-16), b is the coefficient of t (157), and c is the constant term (8).

Plugging in the values, we get:

t = (-157 ± √(157^2 - 4(-16)(8)))/(2(-16))

Simplifying the equation further:

t = (-157 ± √(24649 + 512))/(2(-16))

t ≈ (-157 ± √(25161))/(2(-16))

t ≈ (-157 ± 158.7)/(2(-16))

Now, we can calculate the two solutions:

t ≈ (-157 + 158.7)/(-32)

t ≈ 1.7/(-32) ≈ -0.0531

t ≈ (-157 - 158.7)/(-32)

t ≈ -315.7/(-32) ≈ 9.87

Since time cannot be negative in this context, we discard the negative solution.

Therefore, the arrow will hit the ground approximately 9.9 seconds after it was shot.